A vertical right-circular cylindrical tank measures 28 ft high and 14 ft in diameter. It is full of liquid weighing 62.4 lb/ft³. How much work does it take to pump the liquid to the level of the top of the tank? - Set up the integral that gives the work required, in ft-lb, with y = 0 corresponding to the bottom of the tank. (Type an exact answer, using as needed.)

The power available from a wind turbine is calculated by the following equation: Question Help ▼ P = where P= power [watts], A=sweep area (circular) of the blades [square meters], p= air density [kilograms per cubic meter], and v=velocity [meters per second]. A wind turbine generator has a blade diameter of 380 feet [ft]. The specific gravity of air is 0.00123. Assuming a velocity of 32 miles per hour [mi/h] and the power produced is 4.8 megawatts [MW], determine the efficiency of this turbine. : Click the icon to view the conversion table for length. E Click the icon to view the density of water. E Click the icon to view SI prefixes table. E Click the icon to view the table of common derived units in the SI system. The efficiency of this turbine is | %. (Round your answer to one decimal place.) Enter your answer in the answer box and then click Check Answer. Clear All Check Answer All parts showing hp

Assume that a raindrop has a volume of 0.05 cm^3 and you need an Avogadro's number of raindrops to fill up the cubic water tank. What is the length of the edge of the tank?

Consider a water tank that is being filled with rainfall at the top and is drained through a small hole atthe bottom. The change in volume can be modelled by considering the amount of water entering andleaving the tank (per unit of time) as followsdVdt= fin − fout.Here volume of water in the tank V is in litres, flow rate in fin is in litres per hour, flow rate out fout isin litres per hour and time t is in hours. Initially, the tank contains 50L of water: V (0) = 50.(a) Assume the rainfall throughout the day is getting heavier, such that, fin(t) = 10 + t andthat the tank is losing 10% of its volume of water per hour, such that, fout(V ) = 0.1V . Check bydirect substitution that the functionV (t) = 10(t + 5e−0.1t)satisfies the ODE and the initial condition.Now assume that the hole is slowly growing in size, so that the flow rate out increaseswith time:fout(V, t) = 0.1(1 + 0.1t)V.Solve the ordinary differential equation for V (t) with this flow rate out, using either separation…

Answer for a) is 1.06 x 10^6 J The answer for b) is 4.43 x 10^6 J

A hot tub with a surface area of 28 ft2 is filled with water to a depth of 29 in . Hint: volume is calculated as area × height (A × h). A) What is the volume of water in the tub, in liters? Express your answer to two significant figures and include the appropriate units. B) How many kilojoules are needed to heat the water from 59∘F to 103 ∘F? Express your answer to two significant figures and include the appropriate units. C) If the hot-tub heater provides 5900 kJ/min, how long, in hours, will it take to heat the water in the hot tub from 59∘F to 103∘F? Express your answer to two significant figures and include the appropriate units.